The conformal anomaly induced sector of four-dimensional quantum gravi
ty (ir quantum gravity), which has been introduced by Antoniadis and M
ottola, is studied here on a curved fiducial background. The one-loop
effective potential for the effective conformal factor theory is calcu
lated with accuracy, including terms linear in the curvature. It is pr
oved that a curvature induced phase transition can actually take place
. An estimation of the critical curvature for different choices of the
parameters of the theory is given.